Final answer:
The horizontal component is the projection onto the x-axis, so it should only have an x-coordinate and a 0 for the y-coordinate. Choices provided in the question all contain non-zero y-values, suggesting they are incorrect as none represent the pure horizontal component.
Step-by-step explanation:
The question is focused on identifying the horizontal component of a vector that begins at the origin and terminates at the point (-6,-3) on the Cartesian plane. In a Cartesian coordinate system, the horizontal component or x-component of a vector is the orthogonal projection of the vector onto the x-axis. Therefore, the correct horizontal component of the vector would solely have the x-coordinate of the vector with the y-coordinate being zero. As the point is (-6,-3), the horizontal component would be represented by a vector having the same x-coordinate and a y-coordinate of zero.
Given this information, the correct answer among the choices provided would be:
a. ⟨-6, 0⟩
However, this exact option is not present in the given choices, all of which include non-zero y-values which makes them not purely horizontal. The options provided may be typos or incorrect, as a true horizontal component should not have a y-value other than zero.